面向状态空间模型的无样本持续学习
Exemplar-Free Continual Learning for State Space Models
为视觉骨干网络（如基于 SSM/Mamba 的分类器）提供一种无需样本回放的持续学习正则化手段：直接约束 SSM 可观测子空间的无限时域状态演化，并用 O(n²) 的 Sylvester 方程求解替代 O(n³)，可直接嵌入现有 CL 流程以缓解序列任务中的遗忘。
原文依据 we propose Inf-SSM, a geometry-aware regularization framework for CL in SSMs
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论状态空间模型（SSM）凭借结构化递归在捕捉长程依赖方面表现优异，因而非常适合序列建模。然而，其不断演化的内部状态给持续学习（CL）带来了独特挑战。在无法获取先前任务完整分布的情况下，对状态空间动力学的更新会变得不受约束，从而导致灾难性遗忘。为此，我们提出 Inf-SSM，一种面向 SSM 持续学习的几何感知正则化框架。它通过 SSM 可观测子空间构成的无限维格拉斯曼流形来约束状态演化，且不需要来自先前任务的任何样本。与限制权重更新的经典持续学习方法不同，Inf-SSM 直接对由 SSM 扩展可观测子空间所编码的无限时域状态演化进行正则化。我们表明，施加该正则化需要求解一个称为 Sylvester 方程的矩阵方程，其复杂度通常为 O(n³)。因此，我们利用 SSM 的结构与性质，设计出一种 O(n²) 的求解方案。由此得到一种高效的正则化机制，可无缝集成到现有的持续学习方法中。在 ImageNet-R、CIFAR-100 和 Caltech-256 等具有挑战性的基准上的大量实验表明，该方法在显著减少遗忘的同时，提升了各序列任务上的准确率。
英文原文摘要 1384 字符
State-Space Models (SSMs) excel at capturing long-range dependencies with structured recurrence, making them well-suited for sequence modeling. However, their evolving internal states pose unique challenges in Continual Learning (CL). Without access to the full distribution of previous tasks, updates to the state-space dynamics become unconstrained, leading to catastrophic forgetting. To address this, we propose Inf-SSM, a geometry-aware regularization framework for CL in SSMs. It constrains state evolution via the infinite-dimensional Grassmannian of SSM observability subspaces, without requiring any exemplars from past tasks. Unlike classical CL methods that restrict weight updates, Inf-SSM directly regularizes the infinite-horizon state evolution encoded by the extended observability subspace of the SSM. We show that enforcing this regularization requires solving a matrix equation known as the Sylvester equation, which typically incurs \mathcal O (n^3) complexity. Thus, we develop a \mathcal O (n^2) solution by exploiting the structure and properties of SSMs. This leads to an efficient regularization mechanism that can be seamlessly integrated into existing CL methods. Comprehensive experiments on challenging benchmarks of ImageNet-R, CIFAR-100, and Caltech-256 demonstrate a significant reduction in forgetting while improving accuracy across sequential tasks.